Dynamic induction control is a wind farm flow control strategy that utilises wind turbine thrust variations to accelerate breakdown of the aerodynamic wake and improve downstream turbine performance. However, when floating wind turbines are considered, additional dynamics and challenges appear that make optimal control difficult. In this work, we propose an adjoint optimisation framework for non-linear economic model-predictive control, which utilises a novel coupling of an existing aerodynamic wake model to floating platform hydrodynamics. Analysis of the frequency response for the coupled model shows that it is possible to achieve wind turbine thrust variations without inducing large motion of the rotor. Using economic model-predictive control, we find dynamic induction results that lead to an improvement of 7 % over static induction control, where the dynamic controller stimulates wake breakdown with only small variations in rotor displacement. This novel model formulation provides a starting point for the adaptation of dynamic wind farm flow control strategies for floating wind turbines.

Control-oriented models provide a basis for wind farm control to improve power production and reduce structural loading. Wake steering is considered to be one of the most promising techniques to achieve this. Wind turbine wakes under yaw misalignment are deflected downstream and have been shown to produce a curled or kidney-shaped structure. A Navier-Stokes based code called FRED was developed to model wind farm flow in 2D to perform yaw control. To tackle the differences between 2D and 3D flow, this work introduces a generalised continuity correction and wind turbine force scaling terms to the FRED framework. The effectiveness of approximating 3D results is tested by comparison with 3D simulations in the same framework. The continuity correction is now applicable to general wind directions and effective in reducing wake width and speed-up effects. The magnitude of wake deflection can be tuned using a force scaling term. However, we show that there remains a qualitative difference in the deflection profile downstream, as well as a difference in the propagation of yaw effects over time. From this study we can conclude that there is a fundamental difference between 2D and 3D flow physics in spatial and temporal dynamics which makes the 2D modelling approach challenging for control without further empirical adjustments. The necessary corrections are likely to be complex and non-physical, leading to a departure from the first principles foundation that FRED is developed from.

Wind farm flow control aims to improve wind turbine performance by reducing aerodynamic wake interaction between turbines. Dynamic, physics-based models of wind farm flows have been essential for exploring control strategies such as wake redirection and dynamic induction control. Free-vortex methods can provide a computationally efficient way to model wind turbine wake dynamics for control optimisation. We present a control-oriented free-vortex wake model of a 2D and 3D actuator disc to represent wind turbine wakes. The novel derivation of the discrete adjoint equations allows efficient gradient evaluation for gradient-based optimisation in an economic model-predictive control algorithm. Initial results are presented for mean power maximisation in a two-turbine case study. An induction control signal is found using the 2D model that is roughly periodic and supports previous results on dynamic induction control to stimulate wake mixing. The 3D model formulation effectively models a curled wake under yaw misalignment. Under time-varying wind direction, the optimisation finds solutions demonstrating both wake steering and a smooth transition to greedy control. The free-vortex wake model with gradient information shows potential for efficient optimisation and provides a promising way to further explore dynamic wind farm flow control.

Wind farm flow control (WFFC) is a topic of interest at several research institutes and industry and certification agencies worldwide. For reliable performance assessment of the technology, the efficiency and the capability of the models applied to WFFC should be carefully evaluated. To address that, the FarmConners consortium has launched a common benchmark for code comparison under controlled operation to demonstrate its potential benefits, such as increased power production. The benchmark builds on available data sets from previous field campaigns, wind tunnel experiments, and high-fidelity simulations. Within that database, four blind tests are defined and 13 participants in total have submitted results for the analysis of single and multiple wakes under WFFC. Here, we present Part I of the FarmConners benchmark results, focusing on the blind tests with large-scale rotors. The observations and/or the model outcomes are evaluated via direct power comparisons at the upstream and downstream turbine(s), as well as the power gain at the wind farm level under wake steering control strategy. Additionally, wake loss reduction is also analysed to support the power performance comparison, where relevant. The majority of the participating models show good agreement with the observations or the reference high-fidelity simulations, especially for lower degrees of upstream misalignment and narrow wake sector. However, the benchmark clearly highlights the importance of the calibration procedure for control-oriented models. The potential effects of limited controlled operation data in calibration are particularly visible via frequent model mismatch for highly deflected wakes, as well as the power loss at the controlled turbine(s). In addition to the flow modelling, the sensitivity of the predicted WFFC benefits to the turbine representation and the implementation of the controller is also underlined. The FarmConners benchmark is the first of its kind to bring a wide variety of data sets, control settings, and model complexities for the (initial) assessment of farm flow control benefits. It forms an important basis for more detailed benchmarks in the future with extended control objectives to assess the true value of WFFC.

We aim to improve wind farm control for power output by building on the results from WFSim for the development of a dynamic wind farm model. This model will be part of a closed-loop, economic model-predictive control approach for wind farms. It is constructed from first principles using open-source tools to be suitable for adjoint-based optimisation of turbine yaw angles. In a steady-state inflow configuration with two turbines, the new control model matches power expectations from high fidelity simulations in SOWFA to within 15 %. Under time-varying wind directions, it shows time delays in wake direction as inflow changes propagate through the farm with the wind speed, although the dynamics still differ from the SOWFA reference. The model runs flow simulations for a wind farm with a 3 x 3 array of turbines at a real-time order of magnitude on a regular laptop computer. The new control model shows dynamic flow behaviour as wake changes propagate through the wind farm. Some further adjustments are necessary to accurately model three-dimensional flow in two dimensions. With more validation of the wake dynamics, it will be suitable for application in a new closed-loop wind farm controller.